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We experimentally and numerically demonstrate dodecagonal and decagonal quasiperiodic photonic crystals in the microwave region. The results show that only a small number of rows are needed to create a frequency gap in the transmission spectrum, and that the gap position is insensitive to the incident angle. In particular, there is no defect state at the first gap of a dodecagonal quasiperiodic photonic crystal when there is a cavity in the center region, even though the cavity volume is much larger than the square of the wavelength. The decagonal quasiperiodic crystal can offer great possibilities for creating defect states. These quasiperiodic photonic crystals may find some important applications in photoelectric devices.

The transmission spectra at the high-symmetry points of the first Brillouin zone are measured for three face-centered-cubic colloidal crystals made of silica spheres of different submicrometer sizes. It is found that at the $U$ point the transmission dip exists not only for an $s$ wave, but also for a $p$ wave. Moreover, at the $W$ point the transmission dips of both $s$ and $p$ waves appear at the same wavelength. Our calculations confirm that these dips correspond to the lowest band gaps of the high-symmetry points. The structures and parameters of these crystals are determined by the Kossel-rings analysis as well as by the transmission spectra.

In this paper, we study negative refraction of electromagnetic waves in three-dimensional (3D) inverse opal photonic crystals (PCs). We employ the plane-wave expansion method to calculate the equifrequency surface of the PC structure, from which the frequency window where negative refraction might occur can be determined. We then investigate the propagation of electromagnetic waves radiating from a point source through a flat PC slab by means of a finite-difference time-domain method. We find that wave focusing can be achieved in such a 3D inverse opal PC structure at the negative-refraction frequency window. Because the inverse opal photonic crystal can be routinely synthesized in the optical regime by means of the self-assembly approach, our study opens a way for realization and application of 3D negative-refraction superlenses in the visible and infrared regimes.

We use near-field scanning optical microscopy (NSOM) operating in collection mode to map the optical field distribution of continuous wave infrared light propagating along an air-bridged W3 silicon photonic crystal (PC) slab multimode waveguide in a subwavelength resolution. The detected near-field optical intensity distribution patterns show very different longitudinal propagation features and transverse field profiles at different wavelength ranges. We have analyzed the dispersion of the guided modes in the PC waveguide and the corresponding eigenfield profile for each guided mode by means of the three-dimensional plane-wave expansion simulations. It is found that the experimentally observed complex while interesting near-field pattern features can be well explained by the field profiles of the multiple waveguide modes and their superposition at different excitation wavelengths. The detection and analysis of this multimode PC slab waveguide via NSOM could help us to understand complex wave propagation behavior and to further design novel PC devices.

The periodic arrays of two-stage cross-dipole fractal slits etched on a $200\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick gold film exhibit two resonance pass bands in the near- and mid-infrared region. The sample was fabricated by electron beam lithography and reactive ion etching system, and the width of the fractal slits is about $120\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The transmission coefficient exceeds 1 at the peak wavelength if normalized to the area of the fractal slits. The measured transmission spectrum in the frequency domain around the short wavelength pass band agrees well with the simulation results obtained via the transfer-matrix method. The existence of two resonance bands and their relative positions can be well explained by the geometric self-similarity of the fractal structure. Both transmission spectrum and electric field distribution analysis show that the two resonance bands result from the interaction of the incident light with the individual primary and secondary elements of the two-stage fractal structure.

We have experimentally investigated the negative refraction and focusing by a two-dimensional photonic crystal (PC) made from a triangular lattice of metal-core dielectric-shell coated cylinders. At a certain frequency, the PC structure has an isotropic band at which the phase velocity is antiparallel to the group velocity. As a result, the PC structure can exhibit negative refraction and the corresponding effective refractive index can be close to the ideal value of $\ensuremath{-}1$. A flat lens formed from such a PC has been designed and its imaging properties have been investigated systematically. The measurement results show that the flat lens can form non-near-field images, and the source and image distance follow the conventional wave-beam negative refraction law for the refractive index of $\ensuremath{-}1$ irrespective of the slab thickness and the source distance.

Imaging properties of a photonic-crystal (PC) slab lens consisting of a square lattice of elliptical dielectric rods in air are studied theoretically. The finite-difference time-domain technique is used to investigate the field patterns of a TM-polarized point source placed in the vicinity of the PC slab. A good-quality image can form in the opposite side of the slab in a frequency window located slightly below the fundamental band gap, but it is strongly confined in the near-field region irrespective of change of the slab thickness. We have changed the orientation of the elliptical rods with respect to the surface normal of the slab, and found that when the major or minor axis of the rods is not collinear with the surface normal, the image spot can show a vertical shift away from the horizontal line passing the point source. The simulation results are consistent with the equifrequency-surface contour analysis for these elliptical-rod photonic-crystal structures.

The transmission property and localization of electromagnetic waves in defect free dodecagonal quasiperiodic photonic crystals (QPCs) are studied. The simulation of total energy flow and the density of states show that the dodecagonal QPC has a photonic gap for TM polarized electromagnetic waves. However, different from the periodic photonic crystals, electromagnetic waves with certain frequencies are localized at some special regions inside a perfect dodecagonal QPC. A corresponding experiment in the microwave region confirms the phenomenon. It is believed that the occurrence of localized modes in QPCs can be attributed to the competition between two spatial structural properties: self-similarity and nonperiodicity.

A decomposition scheme for probing the total density of states (DOS) in an arbitrary photonic crystal (PC) having luminescent molecules is suggested. Some number distributions of the luminescent molecules can partially probe DOS information or even all the details of the total DOS by measuring the dynamic characteristics of the spontaneous decay of excited luminescent molecules in a PC. One can probe the total DOS directly when the ratio of the number densities of the homogeneously dispersed luminescent molecules in the scatterers and in the background material is equal to the ratio of the dielectric constants of the scatterer and the background material.